dampingStd

The module freezes one-member GWTC-3 ringdown statistics after mapping the usual QNM parameters $(f_{t_0},\tau_{t_0})$ to the dimensionless per-cycle damping ratio $\exp(-1/(f_{t_0}\tau_{t_0}))$. Recognition Science supplies a structural echo-damping target $1/\varphi\approx 0.618$, with $\varphi$ the golden ratio fixed by the self-similarity step of the forcing chain.

Sibling constants in the same file hold the mean, median, and central quantiles (5%, 16%, 84%, 95%) of that derived posterior for the range-read file rin/rin_S190727h_pyring_DS_1mode_10M.h5. The present definition is the corresponding sample standard deviation, used only as a width scale for residual and $z$-score comparisons against the RS target.

Status is structural and closed: zero sorry, no new RS axioms. The comparison is explicitly one-member and does not identify single-mode QNM damping with the full RS echo-train observable.

Definitional constant: the real literal $0.220115833630$ is assigned directly. No lemma applications, no tactics, no reduction. The number is the precomputed sample standard deviation of the mapped damping-per-cycle draws from the named HDF5 summary.

Gives the width scale against which the RS structural target $1/\varphi$ is judged for this GWTC-3 member. Downstream residual and $z$-from-mean quantities in the same module (and any later multi-member aggregation) need a frozen $\sigma$ so that "target inside the central 68%/90% interval" is a pure numeric check rather than a re-reduction of the HDF5 sample.

In the broader Recognition framework this sits in the verification layer: it does not re-derive $\varphi$ or the eight-tick structure, but supplies an observational width for the claim that the RS echo-damping scale lies inside the posterior band of at least one published ringdown member. The module doc already flags the open gap: single-mode QNM damping per cycle is not yet identified with the final RS echo-train damping observable, and the result is not archive-wide.